2v^2+7v+34=v^2-4v+4

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Solution for 2v^2+7v+34=v^2-4v+4 equation: 


Simplifying
2v2 + 7v + 34 = v2 + -4v + 4

Reorder the terms:
34 + 7v + 2v2 = v2 + -4v + 4

Reorder the terms:
34 + 7v + 2v2 = 4 + -4v + v2

Solving
34 + 7v + 2v2 = 4 + -4v + v2

Solving for variable 'v'.

Reorder the terms:
34 + -4 + 7v + 4v + 2v2 + -1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Combine like terms: 34 + -4 = 30
30 + 7v + 4v + 2v2 + -1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Combine like terms: 7v + 4v = 11v
30 + 11v + 2v2 + -1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Combine like terms: 2v2 + -1v2 = 1v2
30 + 11v + 1v2 = 4 + -4v + v2 + -4 + 4v + -1v2

Reorder the terms:
30 + 11v + 1v2 = 4 + -4 + -4v + 4v + v2 + -1v2

Combine like terms: 4 + -4 = 0
30 + 11v + 1v2 = 0 + -4v + 4v + v2 + -1v2
30 + 11v + 1v2 = -4v + 4v + v2 + -1v2

Combine like terms: -4v + 4v = 0
30 + 11v + 1v2 = 0 + v2 + -1v2
30 + 11v + 1v2 = v2 + -1v2

Combine like terms: v2 + -1v2 = 0
30 + 11v + 1v2 = 0

Factor a trinomial.
(6 + v)(5 + v) = 0


Subproblem 1
Set the factor '(6 + v)' equal to zero and attempt to solve:

Simplifying
6 + v = 0

Solving
6 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + v = 0 + -6

Combine like terms: 6 + -6 = 0
0 + v = 0 + -6
v = 0 + -6

Combine like terms: 0 + -6 = -6
v = -6

Simplifying
v = -6

Subproblem 2
Set the factor '(5 + v)' equal to zero and attempt to solve:

Simplifying
5 + v = 0

Solving
5 + v = 0

Move all terms containing v to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + v = 0 + -5

Combine like terms: 5 + -5 = 0
0 + v = 0 + -5
v = 0 + -5

Combine like terms: 0 + -5 = -5
v = -5

Simplifying
v = -5
Solution
v = {-6, -5}

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